On the Reduction of Associate Classes for the PBIB Design of a Certain Generalized Type
The Annals of Statistics · 1974 · Volume 2 · Issue 6
Abstract
For BIB designs $N_i$ and their complements $N_i^\ast (i = 1,2, \cdots, n)$, Kageyama (1972) gave necessary and sufficient conditions for a PBIB design $N = N_1 \otimes N_2 + N_1^\ast \otimes N_2^\ast$ with at most three associate classes having the rectangular association scheme to be reducible to a PBIB design with only two distinct associate classes having the $L_2$ association scheme. In this paper similar results for the PBIB design $N_1 \otimes N_2 \otimes \cdots \otimes N_n + N_1^\ast \otimes N_2^\ast \otimes \cdots \otimes N_n^\ast$, which is in a sense a generalization of the Kronecker products of the above type, are described.
Keywords
05B20, 62K10, association scheme, BIB design, coincidence number, Kronecker product, PBIB design
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